Operator Overloading Matrix Multiplication - c++

Question

The issue I am having is how to get the correct number columns to go through for the inner most loop of K.
An example is a 2x3 matrix and a 3x2 matrix being multiplied.
The result should be a 2x2 matrix, but currently I dont know how to send the value of 2 to the operator overloaded function.
It should be
int k = 0; k < columns of first matrix;k++
Matrix::Matrix(int row, int col)
{
rows = row;
cols = col;
cx = (float**)malloc(rows * sizeof(float*)); //initialize pointer to pointer matrix
for (int i = 0; i < rows; i++)
*(cx + i) = (float*)malloc(cols * sizeof(float));
}
Matrix Matrix::operator * (Matrix dx)
{
Matrix mult(rows, cols);
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
mult.cx[i][j] = 0;
for (int k = 0; k < ?;k++) //?????????????
{
mult.cx[i][j] += cx[i][k] * dx.cx[k][j];
}
}
}
mult.print();
return mult;
//calling
Matrix mult(rowA, colB);
mult = mat1 * mat2;
}

Answer 1

Linear algebra rules say the result should have dimensions rows x dx.cols
Matrix Matrix::operator * (Matrix dx)
{
Matrix mult(rows, dx.cols);
for (int i = 0; i < rows; i++)
{
for (int j = 0; j < cols; j++)
{
mult.cx[i][j] = 0;
for (int k = 0; k < cols;k++) //?????????????
{
mult.cx[i][j] += cx[i][k] * dx.cx[k][j];
}
}
}
mult.print();
return mult;

Answer 2

A few random hints:
Your code is basically C; it doesn’t use (e.g.) important memory-safety features from C++. (Operator overloading is the only C++-like feature in use.) I suggest that you take advantage of C++ a bit more.
Strictly avoid malloc() in C++. Use std::make_unique(...) or, if there is no other way, a raw new operator. (BTW, there is always another way.) In the latter case, make sure there is a destructor with a delete or delete[]. The use of malloc() in your snippet smells like a memory leak.
What can be const should be const. Initialize as many class members as possible in the constructor’s initializer list and make them const if appropriate. (For example, Matrix dimensions don’t change and should be const.)
When writing a container-like class (which a Matrix may be, in a sense), don’t restrict it to a single data type; your future self will thank you. (What if you need a double instead of a float? Is it going to be a one-liner edit or an all-nighter spent searching where a forgotten float eats away your precision?)
Here’s a quick and dirty runnable example showing matrix multiplication:
#include <cstddef>
#include <iomanip>
#include <iostream>
#include <memory>
namespace matrix {
using std::size_t;
template<typename Element>
class Matrix {
class Accessor {
public:
Accessor(const Matrix& mat, size_t m) : data_(&mat.data_[m * mat.n_]) {}
Element& operator [](size_t n) { return data_[n]; }
const Element& operator [](size_t n) const { return data_[n]; }
private:
Element *const data_;
};
public:
Matrix(size_t m, size_t n) : m_(m), n_(n),
data_(std::make_unique<Element[]>(m * n)) {}
Matrix(Matrix &&rv) : m_(rv.m_), n_(rv.n_), data_(std::move(rv.data_)) {}
Matrix operator *(const Matrix& right) {
Matrix result(m_, right.n_);
for (size_t i = 0; i < m_; ++i)
for (size_t j = 0; j < right.n_; ++j) {
result[i][j] = Element{};
for (size_t k = 0; k < n_; ++k) result[i][j] +=
(*this)[i][k] * right[k][j];
}
return result;
}
Accessor operator [](size_t m) { return Accessor(*this, m); }
const Accessor operator [](size_t m) const { return Accessor(*this, m); }
size_t m() const { return m_; }
size_t n() const { return n_; }
private:
const size_t m_;
const size_t n_;
std::unique_ptr<Element[]> data_;
};
template<typename Element>
std::ostream& operator <<(std::ostream &out, const Matrix<Element> &mat) {
for (size_t i = 0; i < mat.m(); ++i) {
for (size_t j = 0; j < mat.n(); ++j) out << std::setw(4) << mat[i][j];
out << std::endl;
}
return out;
}
} // namespace matrix
int main() {
matrix::Matrix<int> m22{2, 2};
m22[0][0] = 0; // TODO: std::initializer_list
m22[0][1] = 1;
m22[1][0] = 2;
m22[1][1] = 3;
matrix::Matrix<int> m23{2, 3};
m23[0][0] = 0; // TODO: std::initializer_list
m23[0][1] = 1;
m23[0][2] = 2;
m23[1][0] = 3;
m23[1][1] = 4;
m23[1][2] = 5;
matrix::Matrix<int> m32{3, 2};
m32[0][0] = 5; // TODO: std::initializer_list
m32[0][1] = 4;
m32[1][0] = 3;
m32[1][1] = 2;
m32[2][0] = 1;
m32[2][1] = 0;
std::cout << "Original:\n\n";
std::cout << m22 << std::endl << m23 << std::endl << m32 << std::endl;
std::cout << "Multiplied:\n\n";
std::cout << m22 * m22 << std::endl
<< m22 * m23 << std::endl
<< m32 * m22 << std::endl
<< m23 * m32 << std::endl
<< m32 * m23 << std::endl;
}
Possible improvements and other recommendations:
Add consistency checks. throw, for example, a std::invalid_argument when dimensions don’t match on multiplication, i.e. when m_ != right.n_, and a std::range_error when the operator [] gets an out-of-bounds argument. (The checks may be optional, activated (e.g.) for debugging using an if constexpr.)
Use a std::initializer_list or the like for initialization, so that you can have (e.g.) a const Matrix initialized in-line.
Always check your code using valgrind. (Tip: Buliding with -g lets valgrind print also the line numbers where something wrong happened (or where a relevant preceding (de)allocation had happened).)
The code could me made shorter and more elegant (not necessarily more efficient; compiler optimizations are magic nowadays) by not using operator [] everywhere and having some fun with pointer arithmetics instead.
Make the type system better, so that (e.g.) Matrix instances with different types can play well with each other. Perhaps a Matrix<int> multiplied by a Matrix<double> could yield a Matrix<double> etc. One could also support multiplication between a scalar value and a Matrix. Or between a Matrix and a std::array, std::vector etc.